Question

a cone has a volume of 2712.96 cubic millimeters and a height of 18 millimeters. what is its radius?
round your answer to the nearest hundredth.
r ≈ millimeters

Explanation:

Step1: Recall the volume formula for a cone

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\), where \(V\) is the volume, \(r\) is the radius and \(h\) is the height.

Step2: Rearrange the formula to solve for \(r^{2}\)

Given \(V = 2712.96\) and \(h=18\), substitute into the formula:
\(2712.96=\frac{1}{3}\pi r^{2}\times18\)
First, simplify the right - hand side: \(\frac{1}{3}\times18 = 6\), so the equation becomes \(2712.96 = 6\pi r^{2}\)
Then, solve for \(r^{2}\): \(r^{2}=\frac{2712.96}{6\pi}\)

Step3: Calculate \(r^{2}\)

Take \(\pi\approx3.14\), then \(r^{2}=\frac{2712.96}{6\times3.14}=\frac{2712.96}{18.84}=144\)

Step4: Calculate \(r\)

Since \(r^{2}=144\), then \(r=\sqrt{144}\) (we take the positive value as radius is non - negative)

Answer:

\(12.00\)